相关论文: Dynamical attractors of memristors and their netwo…

Some memristors are quite interesting from the point of view of dynamical systems. When driven by narrow pulses of alternating polarities, their dynamics has a stable fixed point, which may be useful for future applications. We study the…

Under certain conditions, applying a sequence of voltage pulses of alternating polarities across a resistive switching memory device induces a finite number of fixed-point attractors in its time-averaged dynamics, known as dynamical…

We discuss the physical properties of realistic memristive, memcapacitive and meminductive systems. In particular, by employing the well-known theory of response functions and microscopic derivations, we show that resistors, capacitors and…

The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in…

Neural dynamical systems with stable attractor structures, such as point attractors and continuous attractors, are hypothesized to underlie meaningful temporal behavior that requires working memory. However, working memory may not support…

This paper presents a study of bifurcation in the time-averaged dynamics of TaO memristors driven by narrow pulses of alternating polarities. The analysis, based on a physics-inspired model, focuses on the stable fixed points and on how…

We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…

Memristive devices are commonly benchmarked by the multi-level programmability of their resistance states. Neural networks utilizing memristor crossbar arrays as synaptic layers largely rely on this feature. However, the dynamical…

A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…

Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions…

A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…

In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms…

We present both an overview and a perspective of recent experimental advances and proposed new approaches to performing computation using memristors. A memristor is a 2-terminal passive component with a dynamic resistance depending on an…

We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e.…

Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…

The introduction of a memristor in a chaotic system can significantly modify its dynamical behavior. In this paper, we couple a discrete memristor model with a chaotic map to investigate the memristor's impact on the stability of chaotic…

The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular…

Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for…